Real Madrid registered their first Primera Division victory of the season after a comfortable 3-0 win over Granada at the Bernabeu.
Cristiano Ronaldo bagged a brace, and substitute Gonzalo Higuain was also on target, while the visitors ended the game with ten men after Borja Gomez was sent off after receiving two yellow cards.
Real made three changes from the side who beat Barcelona in the Super Copa clash as new signing Luka Modric came in for Mesut Ozil, Jose Callejon replaced Angel di Maria and Karim Benzema was preferred to Gonzalo Higuain.
Barcelona retained the only 100% record in the league with a fine strike by Adriano sinking struggling Valencia 1-0.
Barca, beaten by rivals Real Madrid in the Supercopa, could have beaten Manuel Pellegrino's side by more goals had Cesc Fabregas not failed to take two good chances.
Tito Vilanova almost saw his side pay for those missed chances as Roberto Soldado and Victor Ruiz both went close, the latter also having a goal disallowed for offside.
Athletic Bilbao put an end to their nightmare start to the season with a comfortable 2-0 win over Valladolid at San Mames.
Marcelo Bielsa's men had conceded nine goals in losing their first two games of the campaign, but put in a far more composed display and were rewarded 20 minutes from time when Aritz Aduriz stroked home his first league goal since returning to the club.
Markel Susaeta then sealed the points five minutes later when he curled beautifully into the top corner after being fed by Inigo Ruiz de Galarreta.
Sevilla missed two penalties as ten-man Rayo Vallecano clung on for a goalless draw to extend an unbeaten start to the Primera Division season.
Alvaro Negredo was first to miss from the spot on seven minutes after Jordi Amat had pulled down the Spanish international inside the area, but he struck the post and the ball rebounded to safety. But the visitors were handed another opportunity 20 minutes from time when Ivan Rakitic was brought down by Ruben Martinez.
The goalkeeper was shown a red card but his replacement Dani Gimenez did not even have to make a save as Rakitic pulled his penalty wide.
Levante netted a stoppage-time goal to cap a stunning 3-2 comeback win against Espanyol and earn their first victory of the campaign.
Espanyol had looked on course to claim their own maiden victory after establishing a 2-0 lead inside the opening 25 minutes through fine efforts from summer signings Samuele Longo and Sergio Tejera.
However, Levante hit back at the start of the second half to draw level with quickfire goals from Juanlu and Christian Lell and then, despite losing striker Vicente Iborra to an 82nd-minute red card, the home side snatched the points when Michel's cross was deflected in three minutes into stoppage time.